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A Noninequality for the Fractional GradientJun 13 2019In this paper we give a streamlined proof of an inequality recently obtained by the author: For every $\alpha \in (0,1)$ there exists a constant $C=C(\alpha,d)>0$ such that \begin{align*} \|u\|_{L^{d/(d-\alpha),1}(\mathbb{R}^d;\mathbb{R}^d)} \leq C \| ... More Spectral semi-Fredholm theory on Hilbert C*-modulesJun 12 2019Given an A-linear, bounded, adjointable operator F on the standard module H_A; we consider the operators of the form F - a1 as a varies over Z(A) and this gives rise to a different kind of spectra of F in Z(A) as a generalization of ordinary spectra of ... More m-isometric operators and their local propertiesJun 12 2019In this paper we give necessary and sufficient conditions for a bounded linear Hilbert space operator to be an $m$-isometry for an unspecified $m$ written in terms of conditions that are applied to "one vector at a time". We provide criteria for orthogonality ... More Amenability and harmonic $L^p$-functions on hypergroupsJun 12 2019Let $K$ be a locally compact hypergroup with a left invariant Haar measure. We show that the Liouville property and amenability are equivalent for $K$ when it is second countable. Suppose that $\sigma$ is a non-degenerate probability measure on $K$, we ... More Torus computed tomographyJun 12 2019We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization ... More On the volume of unit balls of finite-dimensional Lorentz spacesJun 12 2019We study the volume of unit balls $B^n_{p,q}$ of finite-dimensional Lorentz sequence spaces $\ell_{p,q}^n.$ We give an iterative formula for ${\rm vol}(B^n_{p,q})$ for the weak Lebesgue spaces with $q=\infty$ and explicit formulas for $q=1$ and $q=\infty.$ ... More An Optimal Plank TheoremJun 10 2019It is shown that for any sequence $v_1,v_2,\dots,v_n$ of unit vectors in a real Hilbert space $H$, there exists a unit vector $v$ in $H$ such that $$|\langle v_k,v \rangle| \geq \sin(\pi/2n)$$ for all $k$. This a sharp version of the plank theorem for ... More Dot product invariant valuations on Lip$(S^{n-1})$Jun 10 2019We provide an integral representation for continuous, rotation invariant and dot product invariant valuations defined on the space Lip$(S^{n-1})$ of Lipschitz continuous functions on the unit $n-$sphere. On the Riesz Transforms for the inverse Gauss measureJun 10 2019Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian function. Let further $\mathscr{A}$ be the natural self-adjoint Laplacian on $L^2(\gamma_{-1})$. In this paper, we prove that the Riesz ... More Norms of weighted sums of log-concave random vectorsJun 09 2019Let $C$ and $K$ be centrally symmetric convex bodies of volume $1$ in ${\mathbb R}^n$. We provide upper bounds for the multi-integral expression \begin{equation*}\|{\bf t}\|_{C^s,K}=\int_{C}\cdots\int_{C}\Big\|\sum_{j=1}^st_jx_j\Big\|_K\,dx_1\cdots dx_s\end{equation*} ... More A note on norms of signed sums of vectorsJun 09 2019Our starting point is an improved version of a result of D. Hajela related to a question of Koml\'{o}s: we show that if $f(n)$ is a function such that $\lim\limits_{n\to\infty }f(n)=\infty $ and $f(n)=o(n)$, there exists $n_0=n_0(f)$ such that for every ... More Decomposition of the tensor product of two Hilbert modulesJun 09 2019Given a pair of positive real numbers $\alpha, \beta$ and a sesqui-analytic function $K$ on a bounded domain $\Omega \subset \mathbb C^m$, in this paper, we investigate the properties of the sesqui-analytic function $\mathbb K^{(\alpha, \beta)}:= K^{\alpha+\beta}\big(\partial_i\bar{\partial}_j\log ... More Banach limits -- Some new thoughts and perspectivesJun 09 2019The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional analysis as ... More Roe- Strichartz Theorem on Two Step Nilpotent Lie GroupsJun 08 2019Strichartz characterized eigenfunctions of the Laplacian on Euclidean spaces by boundedness conditions which generalized a result of Roe for the one-dimensional case. He also proved an analogous statement for the sublaplacian on the Heisenberg groups. ... More Twin semigroups and delay equationsJun 08 2019In the standard theory of delay equations, the fundamental solution does not `live' in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators and this, ... More Semi-Fredholm Theory on Hilbert C*-modulesJun 07 2019In this paper we establish the semi-Fredholm theory on Hilbert C*-modules as a continuation of Fredholm theory on Hilbert C*-modules established by Mishchenko and Fomenko. We give a definition of a semi-Fredholm operator on Hilbert C*-module and prove ... More Planar sampling sets for the short-time Fourier transformJun 07 2019This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particular, we give a quantitative estimate for the lower sampling bound in the ... More The forward and backward shift on the Lipschitz space of a treeJun 06 2019We initiate the study of the forward and backward shifts on the Lipschitz space of a tree, $\mathcal L$, and on the little Lipshitz space of a tree, ${\mathcal L}_0$. We determine that the forward shift is bounded both on $\mathcal L$ and on ${\mathcal ... More Holomorphic functions with large cluster setsJun 05 2019We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed unit ball of ... More Reflexivity and non-weakly null maximizing sequencesJun 05 2019We introduce and explore a new property related to reflexivity that plays an important role in the characterization of norm attaining operators. We also present an application to the theory of compact perturbations of linear operators and characterize ... More Estimates for matrix coefficients of representationsJun 05 2019Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis and Mautner, and by Kunze and Stein. Two types of estimates have been established: ... More Some remarks on $L^1$ embeddings in the subelliptic settingJun 05 2019In this paper we establish an optimal Lorentz estimate for the Riesz potential in the $L^1$ regime in the setting of a stratified group $G$: Let $Q\geq 2$ be the homogeneous dimension of $G$ and $\mathcal{I}_\alpha$ denote the Riesz potential of order ... More A Note on Estimates for Elliptic Systems with $L^1$ DataJun 04 2019In this paper we give necessary and sufficient conditions on the compatibility of a $k$th order homogeneous linear elliptic differential operator $\mathbb{A}$ and differential constraint $\mathcal{C}$ for solutions of \begin{align*} \mathbb{A} u=f\quad\text{subject ... More Hoeffding decomposition in $H^1$ spacesJun 04 2019The well known result of Bourgain and Kwapie\'n states that the projection $P_{\leq m}$ onto the subspace of the Hilbert space $L^2\left(\Omega^\infty\right)$ spanned by functions dependent on at most $m$ variables is bounded in $L^p$ with norm $\leq ... More Toeplitz operators and pseudo-extensionsJun 04 2019There are three main results in this paper. First, we find an easily computable and simple condition which is necessary and sufficient for a commuting tuple of contractions to possess a non-zero Toeplitz operator. This condition is just that the adjoint ... More Complex interpolation of families of Orlicz sequence spacesJun 03 2019We show that under general conditions complex interpolation of a family of Orlicz sequence spaces gives rise to an Orlicz sequence space, and compute the centralizer induced by the differential process, generalizing results for complex interpolation of ... More Localized John--Nirenberg--Campanato SpacesJun 03 2019Let $p\in(1,\infty)$, $q\in[1,\infty)$, $s\in{\mathbb Z}_{+}$, $\alpha\in[0,\infty)$ and $\mathcal{X}$ be $\mathbb R^n$ or a cube $Q_0\subsetneqq\mathbb R^n$. In this article, the authors first introduce the localized John--Nirenberg--Campanato space ... More Resistance matrices of directed graphsJun 03 2019Let $G$ be a strongly connected and balanced directed graph. The Laplacian matrix of $G$ is then the non-symmetric matrix $L:=D-A$, where $A$ is the adjacency matrix of $G$ and $D$ is the diagonal matrix such that the row sums and the column sums of $L$ ... More Resistance matrices of directed graphsJun 03 2019Jun 12 2019Let $G$ be a strongly connected and balanced directed graph. The Laplacian matrix of $G$ is then the matrix (not necessarily symmetric) $L:=D-A$, where $A$ is the adjacency matrix of $G$ and $D$ is the diagonal matrix such that the row sums and the column ... More Matrix methods for wave equationsJun 02 2019In analogy to a characterisation of operator matrices generating $C_0$-semigroups due to R. Nagel (\cite{[Na89]}), we give conditions on its entries in order that a $2\times 2$ operator matrix generates a cosine operator function. We apply this to systems ... More Monotone Relations in Hadamard SpacesJun 02 2019In this paper, the notion of $\mathcal{W}$-property for subsets of $X\times X^\loze$ is introduced and investigated, where $X$ is an Hadamard space and $X^\loze$ is its linear dual space. It is shown that an Hadamard space $X$ is flat if and only if $X\times ... More On slow decay of Peetre's K-functionalJun 02 2019We characterize when Peetre's K-functional decays to zero slowly and we use this characterization to demonstrate certain strict inclusions between real interpolation spaces. On $k$ point density problem for band-diagonal $M$-basesJun 01 2019In the early 1990s the works of Larson, Wogen and Argyros, Lambrou, Longstaff disclosed an example of a strong tridiagonal $M$-basis that was not rank one dense. Later Katavolos, Lambrou and Papadakis studied $k$ point density property of this example. ... More Kernel Instrumental Variable RegressionJun 01 2019Instrumental variable regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available ... More Convex Quadratic Equations and FunctionsJun 01 2019Three interconnected main results (1)-(3) are presented in closed forms. (1) Regarding the convex quadratic equation (CQE), an analytical equivalent solvability condition and parameterization of all solutions are completely formulated, in a unified framework. ... More Vertical versus horizontal Sobolev spacesMay 31 2019Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi ... More On some local Bishop-Phelps-Bollobás propertiesMay 31 2019We continue a line of study about some local versions of Bishop-Phelps-Bollob\'as type properties for bounded linear operators. We introduce and focus our attention on two of these local properties, which we call L$_{p, o}$ and L$_{o, p}$, and we explore ... More The general linear equation on open connected setsMay 31 2019Fix non-zero reals $\alpha_1,\ldots,\alpha_n$ with $n\ge 2$ and let $K$ be a non-empty open connected set in a topological vector space such that $\sum_{i\le n}\alpha_iK\subseteq K$ (which holds, in particular, if $K$ is an open convex cone and $\alpha_1,\ldots,\alpha_n>0$). ... More Analytic P-ideals and Banach spacesMay 31 2019We study the interplay between Banach space theory and theory of analytic P-ideals. Applying the observation that, up to isomorphism, all Banach spaces with unconditional bases can be constructed in a way very similar to the construction of analytic P-ideals ... More Generality of Lieb's Concavity TheoremMay 30 2019We show that Lieb's concavity theorem holds more generally for any unitarily invariant matrix function $\phi:\mathbf{H}^n_+\rightarrow \mathbb{R}$ that is monotone and concave. Concretely, we prove the joint concavity of the function $(A,B) \mapsto\phi\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big] ... More Some Remarks on Schauder Bases in Lipschitz Free SpacesMay 30 2019We show that the basis constant of every retractional Schauder basis on the Free space of a graph circle increases with the radius. As a consequence, there exists a uniformly discrete subset $M\subset\mathbb{R}^2$ such that $\mathcal F(M)$ does not have ... More On the Operator Jensen Inequality for Convex FunctionsMay 30 2019This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed ... More On the Operator Jensen Inequality for Convex FunctionsMay 30 2019Jun 07 2019This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed ... More Riesz Decompositions for Schrödinger Operators on GraphsMay 29 2019We study superharmonic functions for Schr\"odinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into ... More A $ξ$-weak Grothendieck compactness principleMay 29 2019For $0\leqslant \xi\leqslant \omega_1$, we define the notion of $\xi$-weakly precompact and $\xi$-weakly compact sets in Banach spaces and prove that a set is $\xi$-weakly precompact if and only if its weak closure is $\xi$-weakly compact. We prove a ... More Passive discrete-time systems with a Pontryagin state spaceMay 29 2019Passive discrete-time systems with Hilbert spaces as an incoming and outgoing space and a Pontryagin space as a state space are investigated. A geometric characterization when the index of the transfer function coincides with the negative index of the ... More Quaternionic Regularity via Analytic Functional CalculusMay 29 2019Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic approach. ... More On the numerical index with respect to an operatorMay 29 2019Given Banach spaces $X$ and $Y$, and a norm-one operator $G\in \mathcal{L}(X,Y)$, the numerical index with respect to $G$, $n_G(X,Y)$, is the greatest constant $k\geq 0$ such that $$\max_{|w|=1}\|G+wT\|\geq 1 + k \|T\|$$ for all $T\in \mathcal{L}(X,Y)$. ... More